Conversion of adaptively sampled distance fields to triangles

ABSTRACT

A method for converts an adaptively sampled distance field of a graphics model to a triangle model, The adaptively sampled distance field includes surface cells storing distance values that have corresponding gradients. A vertex is assigned to a center location of each surface cell. The vertices of neighboring surface cells are connected to form triangles while satisfying a predetermined constraint. Then, each vertex is moved, in a single step, to a new location according to the distance value and corresponding gradient of the vertex to substantially conform the triangles to a surface of the model.

FIELD OF THE INVENTION

[0001] The invention relates generally to the field of shaperepresentation, and in particular to the conversion of sampled distancefields to polygons.

BACKGROUND OF THE INVENTION

[0002] Designing realistic digitized models is a major challenge for theanimation industry, particularly when the models represent characterssuch as people—real or imagined, animals, and cartoon characters.Animation artists generally employ two production methods, alone or incombination. In one method, maquettes are sculpted from a traditionalmedium like clay and then digitized. In another method, the models areconstructed using one of several commercial or custom computerizedmodeling systems, such as MAYA, SoftImage, 3DStudioMax, FormZ, andHoudini.

[0003] Clay is the medium of choice for most animation artists becauseit is expressive, and working with clay is intuitive. It is difficult toimprove on clay as the ideal modeling medium. A standard approach fordesigning clay-based digital models involves sculpting a clay maquetteand digitizing or scanning the maquette to generate the digital model.There is a plethora of systems for scanning objects and generatingsurface models from the scanned data.

[0004] However, sculpting with clay and then digitizing the claymaquette has several limitations for digital animation. Much detail canbe lost in the digitizing process because scanners and digitizers haveinherent limitations in resolution, are unable to digitize occluded orhard-to-reach surfaces, and are subject to noise. Thus, some of theadvantages of clay are lost in the scanning process. Furthermore,long-term storage of the clay models is difficult. It is important tonote, however, that scanned models can provide good first orderapproximations to the geometry of the clay maquettes that can then beenhanced by a computer-based modeling system. Hence, it is importantthat any modeling system does accept scanned data as input.

[0005] Most prior art computerized modeling systems typically usepolygons, non-uniform rational B-splines (NURBS), or other subdivisionsof planar surfaces to represent the shape of a model. However, all threerepresentations have limitations.

[0006] Polygon models require a large number of vertices to representdetailed surfaces, particularly when the surfaces are highly curved,textured, or include sharp edges. This makes model generation andediting with polygons cumbersome and time consuming. Because NURBS aretopologically restricted, they must be pieced together to form complexshapes. This presents numerous technical and interface challenges, seeDeRose et al., “Subdivision surfaces in character animation,” Proc.SIGGRAPH '98, pp. 85-94, 1998. While subdivision of planar surfaces doesnot suffer from the same topological restrictions as NURBS, controllingshape changes, and adding fine detail during editing are difficult. Asanother problem, all of these modeling techniques are only surfacerepresentations—the models are nothing more than hollow shells andnothing is known about interior portions.

[0007] Even worse, sculpting of surface representations can lead tomodels that are not “watertight.” For example, seams where differentresolution NURBS are joined can separate to form annoying cracks andholes. This means that the sculpted models have to be carefullyinspected and edited before a watertight finished product is produced.Watertight models are important for several applications such as rapidprototyping technologies including stereo lithography.

[0008] All computerized modeling systems usually perform editing bymanipulating control vertices. This requires significant skill andpatience, as well as foresight and careful planning to ensure that themodels have enough control vertices where detail is desired. For thesereasons, computerized modeling systems do not rival the intuitive andexpressive nature of clay.

[0009] To make the manipulation more intuitive, most modeling systemsallow the user to interact with groups of control vertices using acomputer implemented (digital) sculpting tool. For example, in MAYAArtisan, NURBS models are modified via a brush tool that manipulatesgroups of control vertices. Operations for pushing, pulling, smoothing,and erasing the surface are well known, and the brush tool can affectcontrol vertices in a region of diminishing influence around its center,resulting in a softening of the sculpted shape. The amount of detail inthe sculpted surface depends on the number of control vertices in theregion of the sculpting tool. Finer control requires more subdivision ofthe NURBS surface, resulting in a less responsive system and a largermodel. Often, mesh subdivision is user controlled and preset. It doesnot adapt to tool selection, or the detail of the sculpted surface.Hence, achieving fine detail in desired regions without excessivesubdivision of the surface in other regions requires significantforesight and planning.

[0010] SoftImage provides a sculpting interface, called “Meta-Clay,”that is similar to the “metaballs” technology as described by Wyvill etal. in “Animating soft objects,” the Visual Computer, 2(4):235-242,1986. Meta-Clay is a density based representation for modeling organic,sculpted objects. This representation produces blobby shapes, and doesnot represent edges, corners, or fine detail.

[0011] Sculpting of parametric models are described by Fowler,“Geometric manipulation of tensor product surfaces,” Proc. of the 1992Symposium on Interactive 3D Graphics, pp. 101-108, 1992, Khodakovsky etal. “Fine Level Feature Editing for Subdivision Surfaces,” ACM SolidModeling Symposium, 1999, and Terzopoulos et al. “Dynamic NURBS withgeometric constraints for interactive sculpting,” ACM Transactions OnGraphics, 13(2), pp. 103-136, 1994. However, each of these suffers fromsome of the limitations described above, and none attain sculptedresults of the quality required for the animation industry.

[0012] To address the problems of polygon, NURBS, and other surfacesubdivision representations, volumetric data structures can be used.These data structures can be generated parametrically or by samplingtechniques using, for example, laser or other ranging techniques, orscanners that penetrate the object to be modeled. Volumetric data canrepresent both the exterior and interior portions of models. Thevolumetric data are then sculpted by applying digital sculpting tools.The tools modify sample values near where the sculpting tool interactswith the volume. For these reasons, sampled volumes hold more promise asa data structure for digital clay.

[0013] FreeForm is a commercial system for sculpting volumetric models.FreeForm includes a three degree-of-freedom haptic input device whichuses force feedback to provide the user with a sense of touch whensculpting. Models are represented as regularly sampled intensity values.This greatly limits the amount of detail that can be achieved, andrequires excessive amounts of memory. For example, a minimum systemrequires 512 MB of random access memory (RAM). Intensity values can below-pass filtered to reduce aliasing artifacts in the sculpted models,resulting in smoothed edges and rounded corners typical in volumetricsculpting systems.

[0014] To take advantage of standard hardware rendering engines,volumetric models can be converted to polygon models using a method suchas described by Lorensen et al. in “Marching Cubes: A High Resolution 3DSurface Construction Algorithm,”Proc. SIGGRAPH '87, pp.163-169, 1987.However, with large volume sizes, Marching Cubes produces an excessivenumber of triangles, leading to memory overload and bottlenecks in thegraphics rendering pipeline which limit interactivity.

[0015] There are a number of publications that describe volume-basedsculpting systems including Avila et al. “A haptic interaction methodfor volume visualization,” Proc. IEEE Visualization '96, pp. 197-204,1996, Baerentzen, “Octree-based volume sculpting Proc. Late Breaking HotTopics,” IEEE Visualization '98, pp. 9-12, 1998, Galyean et al.“Sculpting: An Interactive Volumetric Modeling Technique,” Proc.SIGGRAPH '91, pp. 267-274, 1991, and Wang et al. “Volume sculpting,”1995 Symposium on Interactive 3D Graphics, ACM SIGGRAPH, pp. 151-156,1995.

[0016] However, each of these systems suffers from some of thelimitations described above, such as large memory requirements, a fixedresolution determined by the volume size, and soft edges. As a result,such systems are of little use to the high-end digital animationindustry.

[0017] State of the art digital studios, such as Industrial Light andMagic (ILM) and Pixar, have three fundamental requirements for asculpting system that can be used to design animate digital models, suchas animated characters. Animators and artists want digital clay—a mediumwith the characteristics of real clay, (i.e., expressive in its abilityto represent both smooth surfaces and very fine detail, intuitive tosculpt, easy to manipulate, responsive to user input) and the advantagesof a digital media that include the ability to undo, script, duplicate,integrate into digital animation systems, and store permanently. Thesculpting methods should be able to execute on standard computerhardware at interactive rates, and the system must fit into existinganimation production pipelines. That is, the system must be able to readstandard 3D representations or 3D scanned data from clay maquettes, andoutput models compatible with those pipelines.

[0018] The limitations of prior art data structures and modelingsystems, and the needs of the animation industry have been partiallyaddressed by the introduction of adaptively sampled distance fields(ADFs), as described by Frisken et al. in “Adaptively Sampled DistanceFields: A General Representation of Shape for Computer Graphics,” Proc.SIGGRAPH 2000, pp. 249-254, 2000.

[0019] There, ADFs are introduced, basic methods for generating,rendering, and sculpting ADFs are described, and a number ofapplications where ADFs can be used are listed. As an advantage, ADFsstore only as much data as required to represent the detail in anobject.

[0020] Classically, a distance field can be represented as distances,stored in a memory as scalar values. The distances specify minimumdistances to surfaces of an object. When the distances are signed, thesign can be used to distinguish between the inside and outside of theobject. Zero distance values represent the surfaces.

[0021] An adaptively sample distance field (ADF) can be generated byadaptively sampling the object's shape, and storing the sampled distancevalues in a spatial hierarchy for efficient processing.

[0022] Distances at arbitrary points in the ADF can then bereconstructed from the sampled values, and used for computerizedprocessing such as rendering or sculpting. The use of adaptive samplingpermits high sampling rates in regions of fine detail, and low samplingrates where the distance field varies smoothly. Thus, ADFs enable highaccuracy without excessive memory requirements.

[0023] Frisken et al. discuss a basic sculpting procedure for ADFs andoutline methods for generating and rendering ADFs. However, in manyaspects, the prior art ADF manipulation methods are inadequate for aproduction system such as required by the animation industry.

[0024] Specifically, a bottom-up generation method requires too muchmemory and too many distance computations, while a top-down methodrequires time consuming searches for neighbor cells in an octree, andunnecessary repeated recomputation of distance values. Both approachesexhibit poor spatial and temporal memory coherence for cells anddistance values. These memory and processing limitations place practicalrestrictions on the maximum number of ADF levels that can be generated.

[0025] To render ADFs, prior art ray casting methods are sufficientlyfast for small local updates on a desktop Pentium class system. However,ray casting, as known, is too slow for local updates on low-end systems,such as embedded processors in handheld devices, and woefully inadequatefor camera or view changes such as panning, rotation, and zooming. Inaddition, the prior art ADF manipulation methods (1) do not addresseasy-to-use user interfaces for digital sculpting (2) do not provideefficient methods for converting ADFs to standard graphicalrepresentations, such as polygons (3) do not provide any methods forcorrecting distance values other than those at the object's surfaces (4)do not support hardware acceleration, and (5) only discrete steps aresupported during editing.

[0026] However, ADFs could still be an appropriate data structure foruse with a quality sculpting system that meets the needs of digitalstudios if sufficient improvements could be provided. ADFs have a numberof advantages for the entertainment industry. For example, ADFsintegrate volumes and surfaces into a single representation, therebypotentially reducing the number of independent representations requiredby production systems. In addition, ADFs could be combined by simpleconstructive solid geometry (CSG) operations so that individual parts ofa model can be separately modeled, and later joined together. Thisfeature could decrease production costs during model design bymaintaining libraries of model parts and features to quickly and easilydesign new models and characters.

SUMMARY OF THE INVENTION

[0027] The present invention provides an innovative volumetric sculptingsystem that uses adaptively sampled distance fields (ADFs) to enableusers to have better control while orienting and positioning sculptingtools relative to surfaces of digitized models. Distance values are usedto constrain the sculpting tools, and control vertices are used forregion-based conversion to triangles during editing of the model. Inaddition, the sculpted models are always without bothersome cracks andholes making them “watertight.”

[0028] The invention also provides advanced model generating and editingmethods that reduce memory requirements, provide better memorycoherency, and reduced computational costs. Also provided are methodsfor correcting the entire distance field after multiple sculptingoperations.

[0029] The invention also provides several new rendering approaches thattake advantage of hardware acceleration in standard PCs, including fastgeneration of triangles and surface points. Methods for inputting andoutputting models from the system include an improved method forgenerating ADFs from scanned range images, and a new and very fastmethod for generating topologically consistent triangle models from ADFsat various levels of detail (LOD).

[0030] The invention, as described herein, provides animation artistswith an interactive system for sculpting. The system provides the idealmodeling media in the form of digital clay. The system and methods ofthe invention can represent very high resolution shapes at minimalmemory costs, operate with standard computer hardware, and enable easyintegration with existing animation production pipelines.

[0031] Although the sculpting system is designed to meet the demands ofhigh-end production studios, the system also has applications in otherareas of the entertainment industry, such as character design for gamesand virtual reality environments. The system can also be used forindustrial modeling, particularly where the models cannot be generatedparametrically. The ability to output variable level-of-detail modelswith low polygon counts, as required by these applications, enables easyintegration of ADF-based models into existing polygon engines. Inaddition, the modeling methods of the invention can be used by low-endcomputing devices.

[0032] A method for converts an adaptively sampled distance field of agraphics model to a triangle model, The adaptively sampled distancefield includes surface cells storing distance values that havecorresponding gradients. A vertex is assigned to a center location ofeach surface cell. The vertices of neighboring surface cells areconnected to form triangles while satisfying a predetermined constraint.Then, each vertex is moved, in a single step, to a new locationaccording to the distance value and corresponding gradient of the vertexto substantially conform the triangles to a surface of the model.

BRIEF DESCRIPTION OF THE DRAWINGS

[0033]FIG. 1 is a flow diagram of a modeling system according to theinvention;

[0034]FIG. 2 is a diagram of surface following according to theinvention;

[0035]FIGS. 3a-c are diagrams of editing strokes;

[0036]FIG. 4 is a diagram of constrained surface following;

[0037]FIG. 5 is a flow diagram of constrained surface following;

[0038]FIG. 6 is a diagram of control point editing;

[0039]FIG. 7 is a flow diagram of control point editing;

[0040]FIG. 8 is a diagram of a bounded distance tree (BDT) at variousstages during ADF generation;

[0041] FIGS. 9-11 are flow diagrams of BDT generation;

[0042]FIGS. 12a-b are diagrams of interior and exterior points of amodel;

[0043]FIG. 13 is a flow diagram of a scan acquisition procedure;

[0044]FIG. 14 is a flow diagram of a triangulation procedure;

[0045]FIG. 15 is a diagram of cell edges used by the procedure of FIG.14;

[0046]FIGS. 16a-b are diagrams of cracks between edges; and

[0047]FIG. 17 is a flow diagram of an ADF correction method.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0048] System Structure and Components

[0049]FIG. 1 shows a computerized modeling system 100 according to thepresent invention. The modeling system, as a basis, uses adaptivelysampled distance fields (ADFs) 10 to represent digitized models that canbe animated for use by the entertainment industry. The basic datastructure of an ADF is described in U.S. patent application Ser. No.09/370,091 “Detail-Directed Distance Fields” filed by Frisken et al. onAug. 6, 1999, incorporated herein in its entirety by reference. The ADFs10 are used to represent the digitized models. They can also be used torepresent computer implemented tools that operate on the models. Itshould be noted that the tools can add as well as remove material.

[0050] Basic components of the modeling system 100 include a userinterface 101 that provides input data 102 to a bounded distance tree(BDT) generator 103, an editor 104, a renderer 105, a converter 106, apoint generator 107, and a dispatcher 108 which responds to applicationand user requests 109. The system 100 also includes an idle processor110 described in greater detail below. The output data 114 of the systemcan be supplied to industry standard rendering engines, such as OpenGLand RenderMan. The output data 114 can include points, triangles, andimages.

[0051] Data Structures

[0052] The input data 102 include: three-dimensional (3D) models orrange data 131 and generation parameters 132 for the BDT generator 103;edit parameters 141 for the editor 104, a tool path 142 for the editor104; render parameters 151 for the renderer 105; and conversionparameters 161 for the converter 106. The BDT generator 103 operates onbounded distance trees 800 stored in a cache 133. The renderer 105 alsooperates on an intermediate data structure representing image tiles 152generated by adaptive ray casting. The editor 104 and the idle processor110 operate on a script 112 representing intermediate stages of the toolpath 142. The renderer 105, converter 106, and point generator 107operate on images, points and triangles 114 to be processed by therendering engine 111, and the converter 106 generates triangles 115 fromthe ADFs 10.

[0053] System Component and Data Interactions

[0054] The input data 102 is specified by a user with the user interface101. The user sets the parameters 132 for the BDT generator 103, theparameters 141 for the editor 104, the parameters 151 for the renderer104, and the parameters 161 for the converter 106. The user also selectsthe 3D model or range data to be processed by the system 100, the editsto the ADFs 10, and how and when the ADFs are to be converted to thetriangles 115.

[0055] The BDT generator 103 and the editor 104 interact by exchanginglocal regeneration data 135 that include the tool path and modelgeometry. The idle processor interacts with the editor to refine edits136, and with the renderer to refine the rendered image 137. Therenderer interacts with the converter to convert the ADFs 10 totriangles 114.

[0056] System Operation

[0057] During operation of the system 100, the user can start bygenerating an initial model using CSG operations on standard objectshapes such as spheres and boxes, or start by converting a standard 3Dmodel or range data to an ADF. The user then proceeds by sculpting themodel using the editor and selectable sculpting tools.

[0058] As stated above, the sculpting tools can also be represented byADFs, or a simple distance function defining the shape of the tool ifthe shape is simple, for example, spherical. During sculpting, therenderer updates the image tiles 152 while automatically switchingbetween several rendering methods depending on user actions and systemcapabilities.

[0059] During idle-time, the idle processor 110 performs a number ofoperations including increasing the rendering resolution of the imagetiles for the adaptive ray casting, increasing the resolution and extentof edits from the scripted tool paths 112, and correcting distancevalues for points in the ADFs that are not on the surface beingsculpted.

[0060] Interactive Sculpting

[0061] The system 100 includes interactive software for filemanipulation, operation undos, selection, shape smoothing, navigation,and lighting control that are well known to those of ordinary skill inthe art. The description herein focuses on the unique methods of thepresent system for interacting with volumetric data that exploit theproperties of the ADFs 10.

[0062] Surface Following

[0063] As shown in FIG. 2, the system 100 can determine a distance valueand a direction 201 from any point 202 in the adaptively sample distancefield 10 to a nearest point 203 on the surface 204 of the model 200. Thesystem 100 uses this information to guide the path 205 and orientationof a sculpting tool 210, perhaps manipulated by an input means, e.g., amouse or a distance function. The system forces the tool to follow thesurface of the object. It can also, optionally, orient a principal axis211 of the tool 210 to be perpendicular to the model's surface 204.Because the object is represented by an ADF and the tool is representedby an ADF or a distance function, it is possible to determine thedistance between the surface and the tool, the orientation of thesurface, i.e., the direction of the gradient of the object's distancefield, and the principal axis of the tool.

[0064] Surface following is accomplished by iteratively moving the toolin the direction of the gradient of the distance field of the object.The distance moved is an amount proportional to the distance between thetool and the surface, or from some “offset” surface 220 for constrainedsculpting as described below. The offset surface can be external orinternal to the surface of the object. At the same time, the principalaxis 211 of the tool can be aligned with the surface normal of thenearest point on the surface. Surface following is particularly usefulwhen editing a 3D shape with a 2D input device such as a mouse. It canbe difficult to locate the tool accurately on the surface. Surfacefollowing enables more intuitive control when sculpting surfaces thatare oblique to a viewing direction.

[0065] Bezier Tool Paths

[0066] Sculpting can be accomplished by a set of discrete edits alongthe tool's path. However, as illustrated in FIGS. 3a-c, this approachcan be inefficient and erroneous resulting in redundant overlappingedits for slow tool movement (FIG. 3a), and broken edits for fast toolmovement (FIG. 3b). If the shape of the tool is axially asymmetric, thenthe edits can be broken and misaligned when the tool is oblique to thetool's path (FIG. 3c).

[0067] To address these problems, the system edits the ADFs 10 directlywith a swept volume corresponding to the geometry of the tool as thetool moves along a 3D Bezier curve. The system uses a Bezier clippingprocess to compute distances from the curve, and then uses the tool'sgeometry to generate the swept volume, see Nishita et al. in “Raytracing trimmed rational surface patches,” Proc. SIGGRAPH '90, pp.337-345, 1990.

[0068] For a spherical tool, distances in the swept volume are computedby offsetting the distances to the centerline of the tool path. Fortools with rectangular or other shapes, the distance computation is moreinvolved but can still be more efficient than a point-based evaluation.This approach allows two levels of control. First, the Bezier paths canbe automatically derived from the user's input strokes and then carved.Second, the Bezier curve can be explicitly drawn onto the surface of themodel, and edited using control points before the curve is carved ontothe surface.

[0069] Scripting of the Tool Path

[0070] As an advantage, the system 100 records edit paths in the script112 during editing for later processing. The scripted paths providethree important features. First, the editing resolution and the extentof the tool influence on the ADF can be limited in order to achieveinteractive speeds. When this occurs, the scripted edit paths are usedfor lazy evaluation of the edits at higher resolutions, and forincreasing the extent of the tool influence further into the ADF duringidle-time processing. Second, scripted paths provide a history of theediting session, allowing the model to be regenerated on systems withdifferent memory and processing power. Third, the scripted paths,combined with stored intermediate versions of the ADF, enable the systemto process multiple undos without excessive storage. In the preferredembodiment, the script is in the form of a character string or binarydata defining the parameters of the tool's path.

[0071] Dynamic Tools

[0072] The system 100 permits the shape of the tool and its function(add-remove) to vary with time/distance traveled, or according to itslocation on the surface, or according to a description in the tool path.The description can be a procedure which modifies both shape andfunction based on numerous parameters such as time, distance, gradient,surface complexity, and cell geometry.

[0073] Distance-Based Constraints

[0074] As shown in FIG. 4, the system 100 can provide an enhancedmodeling interface because the ADFs 10 represent the distance from themodels' surface to any point in space. The tool can be constrained tomove along the offset surface 220. Thus, the system can force the toolto remove or add material at a specified depth (internal offsetsurface), or height (external offset surface) from the original surface.The computation to keep the tool on the offset surface is as simple asit is to keep the tool on the true surface as described above.

[0075] In addition, the system can use a digital “mask,” 420, also inADF form or as a traditional distance field. The mask can be used in twoways. First, the mask can be used to prevent the tool from modifyingspecified 2D or 3D regions of the model. Second, the tool can be used to“cut-away” portions of the mask, and then only the exposed portions ofthe model are further processed by either adding or removing material.

[0076] The mask can be in the form of a “force field” 430, which canalso be represented as an ADF. The force field's reconstructed distancefield and gradient can provide physical and visual cues, e.g., forcefeedback for haptics, that indicate tool depths or proximity to themodel's surface. Alternatively, the force field can just constrain theediting while the tool is within the “influence” 431 of the force field,that is, the tool is near the mask edges. In addition, multiple masksand force fields can be combined to provide more complex editingconstraints. Note, if the mask constrains the tool to move inside themask region then the force field extends inwards, otherwise the forcefield extends outwards from the mask.

[0077] Applications for Distance-Based Constraints

[0078] Distance-based constraints are useful in many applications. Asdefined by Leler in “Constraint programming languages, theirspecification and generation,” Addison-Wesley Publishing Company, 1988,a constraint is a desired relationship among two or more objects.Industrial designs are often considered to be constraint oriented. Theconstraints of the design usually indicate limitations in the range ofpossible solutions.

[0079] When considering tolerance constraints, which are usually relatedto a single model or surface, the above definition of constraint must beenhanced. Therefore, in the preferred embodiment of the system 100, aconstraint is either imposed on a single model, or represents a desiredrelationship among two or more models.

[0080] An ADF constraint includes at least one ADF, e.g., 420, and aconstraint procedure 440 for instantiating that constraint in the system100. For example, the constraint procedure 440 might absolutely limitthe tool from entering the ADF, as for the mask 420, or limit the tool'smovement when the tool is within a very small specified distance fromthe surface, or limit the tool from entering a region defined by thefield of the ADF, combined with an explicit function that distorts thatfield. In addition, constraints can be combined to form a complexconstraint system.

[0081] One of the novelties in this approach is that constraints can beexpressed as 2D or 3D models which are either converted into ADFs ordrawn directly as ADFs. This representation of constraints as adaptivelysampled distance fields enables constraints to be applied throughoutspace. Associating a procedure with the ADF permits unlimitedflexibility that has particular applications to industrial design. Forexample, if the system is used to design integrated circuits, thensub-micron precision can be obtained easily by specifying constraintswhich guide a tool to the desired accuracy.

[0082] Surface Following Procedure for Distance-Based Constraints

[0083]FIG. 5 shows a procedure 500 that implements distance-basedconstraints of the system 100. Input data to the procedure 500 includeADFs 10 for the model, a tool, masks and/or force fields, constraints501, e.g., desired distance from the surface, and tool orientation andposition parameters 502, e.g., principal axis of tool, and desired anglewith surface. The model, tool, and constraints are manipulated on adisplay device with an input device 503, e.g., a mouse.

[0084] The mouse specifies some current input position (p) 504. Theinput position is transformed 510 to p′ 505 in the coordinate system ofthe ADF. The distance and the gradient 506 at p′ are reconstructed 520.The tool is positioned and oriented 530 to determine a new orientationand position 507, and the tool is displayed 540 to the user.

[0085] Control Point Editing

[0086] While digital sculpting provides a powerful and flexible meansfor digital model design, there are times when control vertexmanipulation has its advantages. For example, to puff or pucker acharacter's cheek, it can be easier to edit a set of control verticesthan to alter the shape of the cheek by adding or removing material withsculpting tools.

[0087] Thus, as shown in FIGS. 6 and 7, the system 100 provides means700 for selecting a portion 610 of the ADF model 10, and converting theselected portion to a polygon (triangular) model 620 with controlvertices at a user controlled level-of-detail, as described below. Thecontrol vertices can then be manipulated, and the edited portion 620 ofthe ADF can be regenerated from the triangle model.

[0088] In the control point editing procedure 700, the input parametersare the ADF 10, and triangulation parameters 701. Step 710 selects ADFcells 711 to triangulate, e.g., the user points at the model's surfaceand identifies the desired portion. The marked cells are triangulated720 as described in further detail below. The triangle mesh 721, at aspecified LOD has an edge on the boundary of the selected portion. Thetriangle mesh is then edited 730, using any known editing procedure. Theedited triangles 731 are locally regenerated 740 to produce the editedADF 630. During the editing and regeneration, the edge of the selectedportion can remain in place to retain a sharp edge, or the edge can berelaxed so that the transition from the selected portion to the rest(unselected) of the surface is smooth.

[0089] Bounded Distance Tree Generation and Editing

[0090] Frisken et al. outline two methods for generating ADFs. Abottom-up method generates a fully populated octree and coalesces cellsupwards when the distance field represented by a cell's eight childrenis well approximated by the sampled distance values of the cell. Atop-down method recursively subdivides cells which do not pass apredicate test comparing distances computed from the model's distancefunction with distances reconstructed from the cell's sampled distancevalues at multiple test points.

[0091] In practical applications, both of these methods have seriouslimitations. The bottom-up approach requires excessive amounts of memoryand too many distance computations to generate high resolution ADFs,while the recursive top-down approach moves up and down through theoctree levels and requires many redundant distance computations andreconstructions. Both approaches exhibit poor memory coherenceminimizing any beneficial effects that could otherwise be obtained fromcaching. Times for generating an ADF with a maximum octree level ofeight (level-8 ADF) is on the order of 20 seconds, and 40 seconds for alevel-9 ADF. This is for a relatively simple CSG model using thetop-down generation method executing on a desk-top Pentium III system.For both methods, generation of ADFs higher than level-9 is impracticaldue to excessive generation time and memory requirements.

[0092] In the present system, the BDT generator 103 balances memoryrequirements, memory coherence, and computation while constructing theADFs. Generation times for similar CSG models are reduced significantlyto less than one second for a level-8 ADF and about two seconds for alevel-9 ADF. This is a 20 times increase in speed over the prior artmethods. Better memory utilization and the faster generator enable thesystem to generate a level-12 ADF in about 8 seconds.

[0093] It should be noted that a level-12 ADF represents a resolutionrange of 1:2⁻¹², i.e., 1:0.00024. Representing this dynamic range in aregularly sampled prior art volume would require about 70 billion samplevalues, clearly beyond the capabilities of most general purposecomputers, and certainly impossible for embedded processors. In sharpcontrast, a typical level-12 ADF requires on the order of 2 to 3 milliondistance values, a considerable improvement, and well within thecapabilities of even small portable devices, such as laptops, personaldigital assistants, and wireless communication devices.

[0094] As shown in FIG. 8, the BDT generator 103 proceeds in a top-downmanner to generate an ADF 10 from a root cell (C₁) 801 in layers,applying recursive subdivision and using bounded distance trees (BDT)800. FIG. 8 shows the octree for a level-12 ADF with layers at level-3803, level-6 806, level-9 809, and level-12 812. The notation C_(n)indicates candidate cells for further subdivision. A layer's depthdetermines the increase in octree depth when the layer is processed. Forexample, a level-9 octree that is generated with a layer depth of threeis generated first to level three, then to level six, and finally tolevel nine.

[0095] Within each layer, the ADF octree is processed one BDT 800 at atime. The BDT can have two, three, or more dimensions. In 2D, the BDTcan be considered a “tile,” and in 3D a “cube.” A BDT is a datastructure used to store computed and reconstructed distances, therebyavoiding redundant distance computations for neighboring cells. In thepreferred embodiment, the BDT is represented as an array in a cache. Asa characteristic, and as shown in FIG. 8, a BDT has a limited depth, andis stored temporarily in the cache while distance values are computed.Each distance value in the BDT has an associated “validity” bitindicating whether or not the distance value is valid. As anothercharacteristic, during normal operation, e.g., editing and sculpting,only “surface” BDTs containing surface cells are processed. BDTs thatare entirely composed of interior and exterior cells are not dealt withuntil the “remote” portions of the distance field are corrected, seeFIG. 17 below.

[0096] The layer depth sets the size of the BDTs. For example, a layerdepth of three, for a 3D model, indicates cubic BDTs of size 2³×2³×2³.When generating a level-9 ADF with a layer depth of three, up to 8³ leafcells are generated in the first layer. When the second layer isprocessed, each leaf cell at level three, as produced from the firstlayer, becomes a candidate for further subdivision and acts as a parentcell of a new BDT. When processing the third layer, each leaf cell atlevel six, produced from the second layer, becomes a candidate forfurther subdivision and so on until a maximum specified level of the ADFis reached or no more candidates remain.

[0097] As an advantage of the invention, computed and reconstructeddistances for each BDT are produced only as needed during recursivesubdivision. In addition, the BDT data structure does not use pointers,as in the ADFs 10, thereby greatly reducing the storage required, andenabling the BDTs to be cached to reduce processing time. Furthermore,when the distance values of the BDT are represented as array elements,rather than a pointer-based tree, access to a distance value requires asingle, constant-time operation.

[0098] A corresponding bit map 1009 associated with each boundeddistance tree 800, see FIG. 10, keeps track of valid distance values inthe BDT 800. The bit map ensures that distance values within the BDT arecomputed and stored only once. There is one validity bit for eachdistance value in the BDT, i.e., each array element.

[0099] After a BDT has been fully processed, valid distances in the BDTare appended to the ADF, and cell pointers to the valid distances areupdated in the ADF. Special care is taken at BDT boundaries byinitializing the BDT 800 and corresponding bit map 1009 from neighboringcells that have already been processed to ensure that distances are alsoshared across neighboring cells of different BDTs, again improvingperformance.

[0100] The size of the BDTs can be adjusted to match the size of thecache 133, see FIG. 1. In Pentium class systems, for example, the BDTstoring up to 83 distance values works effectively, especially when eachdistance value only requires two bytes. The use of the bit map 1009further enhances CPU and cache performance. For example, because the bitmap 1009 stores 32 validity bits in a single memory word on a 32-bitcomputer, the BDT generator can invalidate 32 distance values in a BDTin a single operation. As an advantage, the bounded distance tree datastructure is substantially smaller than the data structure for the ADF.

[0101] The final cells and distances of the ADFs 10 are stored incontiguous arrays of the main memory to further enhance spatialcoherency and performance when processing the ADFs 10 during othersystem operations such as rendering. These arrays are allocated inblocks as needed during BDT generation. The arrays are truncated to amaximum required size when BDT generation completes. Because the arrayblocks are contiguous, updating cell and distance value pointers, whenan ADF is moved or copied in memory, is both fast and easy.

[0102]FIGS. 9, 10, and 11 show steps of a software procedure 900 thatimplements the BDT generator 103. Step 901 allocates blocks of memoryfor cells, distance values (DistVals), the BDT bit map 1009, and the BDT800. Step 1000, see FIG. 10, initializes the fields of a cell andcomputes the cell's error; other processing steps performed with step1000 include initializing a maximum depth level (MaxLevel), invalidatingthe bits in the BDT bit map 1009, and setting a candidate cell(beginning with the root cell 801). A candidate cell is a cell which mayrequire further subdivision. Until there are no more candidate cells902, candidate cells are recursively subdivided 1100, see FIG. 11, toMaxLevel. Valid distance values are copied in step 903, and step 904gets a next candidate cell. At completion, final cells and distancevalues are truncated 905 to a predetermined maximum required size.

[0103] As shown in FIG. 10, the initializing step 1000 includes a step1001 to initialize the fields of the cell, a step 1002 that computes thecell's error measure, and a step 1003 which sets the cell's errormeasure. Note the use of the BDT 800 and its associated bit map 1009 toavoid computing distances already computed.

[0104] The recursive subdivision step 1100 includes the followingsub-steps. A step 1101 excludes interior and exterior cells, i.e., allcells but surface cells, from further subdivision using the distancevalues stored for the corners of the cells, and the diagonal lengths ofthe cells. Step 1102 stops subdividing when the error criterion is met.Step 1103 stops subdividing when the MaxLevel is reached. Step 1104actually performs the subdivision of the cell, and steps 1105 and 1107set the cell type (interior, exterior, and surface) based on the cell'sdistance values. Step 1106 coalesces interior and exterior cells intolarger cells whenever possible.

[0105] Bounded-Surface Generation

[0106] The BDT generation method shown in the FIGS. 8-11 normally onlysubdivides surface cells. This surface-limited generation reduces memoryrequirements while assuring accurate representation of the distancefield in surface cells. This is sufficient for processing regionsimmediately adjacent to the surface.

[0107] However, for some of the editing methods described above, such assurface following, the use of distance-based constraints, and forcefeedback, the distance field is required to be accurate for somedistance from the surface. Under these circumstances, the BDT generationmethod 900 is modified so that exterior and interior cells are notcoalesced unless the cells satisfy a maximum error constraint wheneverthe cells are within a bounded region defined by a specified minimumdistance from the surface. This bounded-surface generation method isunlike the prior art ADF generation techniques.

[0108] Editing

[0109] In the present system, sculpting is performed on the ADFs 10using a local editing process. Compared with prior art ADF processingtechniques, as described by Frisken et al., the use of BDTs according tothe invention decreases edit times by a factor of 20 and reduces memoryrequirements for cells and distance values by a factor of two. Theseadvances make it possible to perform highly detailed sculpting indesktop and portable computer systems.

[0110] To accommodate fewer resources on smaller computer systems, thesystem 100 can limit both the sculpted resolution and the volumetricextent of the tool influence to ensure interactivity. As describedabove, the system 100 maintains a script 112 of sculpting operations andintermediate versions of the ADF. The script 112 can be used duringidle-time processing to increase the sculpting resolution and extend thetool influence into the ADFs 10.

[0111] Correcting Remote Distance Values

[0112] As described above, the ADFs 10 are sculpted by applying CSGoperations to the model and tool distance fields. For example, followingthe positive-inside and negative-outside signed distance valueconvention of Frisken et al., the sculpted distance at a point, p, for adifferencing sculpting tool can be expressed asdist(p)=min(dist_(model)(p), −dist_(tool)(p)), and the sculpted distanceat p for an additive tool is dist(p)=max(dist_(model)(p),dist_(tool)(p)). The use of min/max operators can result in inaccuratedistance values in the ADFs 10 at points in the ADF remote from thesculpted surface, as shown in FIGS. 12a and 12 b.

[0113] For example, as shown in FIGS. 12a and 12 b, a point P1 1201,when using a differencing tool, and the point P2 1202, when using anadditive tool, both would be assigned distances to surfaces that do notexist in the sculpted object, resulting in an inaccurate field at thesepoints. When processing requires only a correct representation of thedistance field at the surface, e.g., during rendering, these inaccuratevalues have no effect.

[0114] However, some of the editing techniques and applications requirean accurate representation of the distance field remote from thesurface. For example, when the system is used for industrial design,sub-micron distance accuracies may be required throughout the volume toproperly guide a tool along a specified path. Hence, the idle processor110 corrects the remote distance field during system idle-time. The idleprocessor 110 can also correct the distance field on-demand in aregion-of-focus, for example, near the working surface of the sculptingtool, to reflect the fact that material is being removed or added.

[0115] There are a number of approaches available for correcting theremote distance field given accurate distances near the model's surface.A fast marching method, derived from level set techniques, can be usedto propagate distances outward from a narrow band of correct values nearthe surface. Another approach holds distance values at the zero-valuediso-surface and the distance field boundaries constant, and usessimulated annealing to smooth out the field in between. Neither of thesemethods are designed for adaptive distance fields, and both methods aretoo slow for interactive editing.

[0116]FIG. 17 shows a method 1700 for correcting remote distance valuesaccording to the invention, for example, during idle processing 110.Step 1701 marks, for each interior/exterior (non-surface) cell, the cellcorner having the minimum, absolute value, distance value. Eachnon-surface cell is also marked as unprocessed. Note, it assumed thatthe distance values of the surface cells are always correct for aparticular error measure, and normally do not need to be corrected.However, it may be desired to change the error measure, for example, forlarge cells through which the surface passes. In this case, these largesurface cells can be selected for “correction.”

[0117] Step 1702 then sorts the interior/exterior cells into ascendingorder using the marked minimum, absolute value, distance values as thesort key. Step 1703 processes the interior/exterior cells in that sortedorder.

[0118] Step 1704 examines each edge of each interior/exterior cell 1711and determines the neighbor cells 1705 that share the edge and that areeither a surface cell or a processed cell, and then step 1707 appendsany missing distance values on the neighboring cell's edge to the sharededge of the interior/exterior cell 1711. Note, distance values canappear anywhere on the shared edge because cells are of varying sizes.

[0119] Then, step 1708 sets the corner values of the interior/exteriorcell 1711, using the newly appended distance values, according to one ofthe correction methods 1710 described below. Finally, step 1708 marksthe cell 1711 as processed, and continues with the next sortedinterior/exterior cell until all interior/exterior cells have beenprocessed.

[0120] Correction Method 1

[0121] Mark each cell corner vertex as “free” or “fixed.” In oneembodiment of the invention, a corner is fixed only if it is a cornershared with a neighboring surface cell, otherwise it is free. In anotherembodiment of the invention, a corner is fixed if it is a corner sharedwith a neighboring surface cell, or processed cell, otherwise it isfree. Then, determine the number of appended distance values associatedwith each corner. An appended distance value is associated with a cornerwhen it is located on an edge connected to that corner, and liesanywhere between the corner and the edge's midpoint. Next, determine thecorner C with the largest number of associated distances. Then, dividethe cell into a uniformly sampled grid at a specified resolution. In apreferred embodiment, the memory required to represent the grid fitsinto the CPU's cache, thereby maximizing performance. Last, perform aEuclidean distance transform on the regular grid propagated from thecorner C and correcting only the free corners of the cell, seeCuisenaire, “Distance Transformations: Fast Algorithms and Applicationsto Medical Image Processing,” Ph.D. thesis, Universite Catholique deLouvain, 1999.

[0122] Correction Method 2

[0123] Determine the nearest newly appended distance D for each freecorner. Then, for each free corner C, determine the Euclidean distance Nto its nearest newly appended distance D. If the distance at C isoutside the range defined by the distance D and the distance N, then setthe distance at C to this range.

[0124] Correction Method 3

[0125] Same as Method 2, but instead of using the nearest newly appendeddistance for each free corner, use all of the newly appended distancesto correct each free corner.

[0126] Correction Method 4

[0127] Use the newly appended distances to derive a corrected distanceat every free corner using extrapolation of distances along an edge orextrapolation of distances throughout the distance field.

[0128] Selecting Interior/Exterior Cells for Correction

[0129] In one embodiment of the invention, step 1701 selects allinterior/exterior cells. In another embodiment of the invention, step1701 selects only those interior/exterior cells within a specifieddistance from the surface. In yet another embodiment of the invention,step 1701 selects only those interior/exterior cells which are immediateneighbors to surface cells. In yet another embodiment of the invention,step 1701 selects only those interior/exterior cells which are within aspecified region, where the region is determined by input from a user,e.g., the location indicated by a mouse event. For some applications,only interior OR exterior cells require correction. In those cases, theinvention limits step 1701 to select only the specified cell type, i.e.,interior OR exterior.

[0130] Selecting Interior/Exterior Cells To Process During BDTGeneration

[0131] Similar criteria listed above for selecting interior/exteriorcells for correction, can be applied to selecting whichinterior/exterior cells are forced to pass the predicate test during BDFgeneration. The predicate test determines if a cell's reconstructionmethod accurately represents the distance field, see Frisken et al. Inone embodiment of the invention, the BDT generator does not require theinterior/exterior cells to pass the predicate test (surface-limitedgeneration). In another embodiment of the invention, the BDT generatorforces interior/exterior cells within a specified distance from thesurface to pass the predicate test (bounded-surface generation). In yetanother embodiment of the invention, the BDT generator forcesinterior/exterior cells which are within a specified region to pass thepredicate test, where the region is determined by input from a user(e.g., the location of mouse events).

[0132] Fast Rendering

[0133] Fast Global Rendering

[0134] The system 100 according to the invention also includes methodsfor converting the ADFs 10 to triangle and point models so that thesystem can be integrated with standard hardware and software implementedrendering engines. Given current standard hardware, such as the NVIDIAGeForce2, these conversion methods provide truly interactivemanipulation of ADFs. For triangles, the ADF is converted to a trianglemodel that can be rendered using the OpenGL rendering engine 111, takingadvantage of hardware triangle rasterization available on many computersystems. The method for converting the ADF to triangles is describedbelow.

[0135] Conversion times are quite fast: the system 100 can generate atriangle model with 200,000 triangles from a level-9 ADF in 0.39s on aPentium IV class processor. Models with lower LODs can be generated evenfaster, e.g., in less than 10 ms for a 2000-triangle model. Thus,triangle models can be generated on-the-fly with imperceptible delayswhen navigation tools are selected, permitting fast global renderingwhile panning, zooming, or rotating the camera.

[0136] Alternatively, the system can use point-based rendering forglobal view changes, taking advantage of the current trend in computergraphics towards hardware-assisted point rendering as described byRusinkiewicz et al. in “Qsplat: A Multiresolution Point Rendering Systemfor Large Meshes,” Proc. SIGGRAPH '00, pp. 343-352, 2000.

[0137] In the preferred embodiment, the system 100 renders points usingthe OpenGL rendering engine 111. The point generator 107 can produce800,000 Phong-shaded points in 0.2 seconds, and less than 0.12 secondsfor unshaded points when shading is performed by the rendering engine111. The points can be rendered interactively on desktop systems and,like triangle models, the points can also be generated on demand whennavigation tools are selected.

[0138] The availability of the distance field and the octree datastructure give ADFs unique advantages for generating points. Forexample, a point randomly generated within a cell can be triviallyprojected onto the surface in one step using the distance value andgradient at that point. Furthermore, the cell size can be used todetermine both the number and size of points to be generated in thatcell, thereby enabling multi-resolution rendering methods.

[0139] Because point generation is very fast, the system can also useview-dependent point generation that culls back-facing cells andback-facing points, and that uses the gradient in the cell to generatemore points on silhouette edges.

[0140] Fast Local Rendering

[0141] The present system uses two methods to locally update the imagein the sculpted region depending on system resources: local trianglegeneration with hardware rendering, and adaptive ray casting forsoftware-based rendering. While point generation is fast enough forlocal editing, point models do not represent fine sculpted detail in theimage as well as triangles or ray casting. Therefore, point models arenot utilized for fast local rendering.

[0142] Local Triangles

[0143] When the ADFs 10 are converted to triangle models for hardwarerendering and there is sufficient memory to maintain both the ADF and atriangle model, the system can locally update these models duringsculpting. To enable local updating, triangles are indexed according tothe cells from which they are generated. When a cell is affected bysculpting, its associated triangles are deleted and new triangles aregenerated, on-the-fly, during the sculpting process. This method is veryfast but requires additional memory per cell for triangle indexing aswell as memory for maintaining the dynamic triangle model.

[0144] Adaptive Ray Casting

[0145] The system 100 provides ray casting for high quality rendering ofthe sculpted surface. When this method is used during sculpting, theimage is updated locally within the region affected by the tool.

[0146] For applications that cannot perform software-based ray castingfast enough for interactive updating, the system 100 uses an adaptiveray casting approach 152 to produce an image representation of the modelat a particular viewpoint. The ray casting approach is an extension ofdirectional coherence maps (DCM) described by Guo in “ProgressiveRadiance Evaluation Using Directional Coherence Maps,”Proc. SIGGRAPH'98, pp. 255-266, 1998.

[0147] The image region to be updated is divided into a hierarchy ofimage tiles, and subdivision of the image tiles is guided by aperceptually based predicate. Pixels within image tiles that have notbeen fully subdivided are bi-linearly interpolated to produce the image.

[0148] For each image tile, rays are cast into the ADF 10 at tilecorners and intersected with the surface using a linear intersectionmethod. The predicate used to test for further subdivision is based on amethod described by Mitchell in “Generating antialiased images at lowsampling densities,” Proc. SIGGRAPH '87, pp. 65-72, 1987.

[0149] Mitchell individually weights the contrast in red, green, andblue channels, and the variance in depth-from-camera across the imagetile. The adaptive ray casting approach 152 according to the inventiontypically achieves a 6:1 reduction in rendering times over casting oneray per pixel, and more than a 10:1 reduction when the image issuper-sampled for anti-aliasing.

[0150] Adapting the Sculpting System to a Character Animation Pipeline

[0151] Any sculpting system that uses a novel data representation fordigital model design is useless to a production system unless thesculpting system can be integrated with existing rendering pipelines.These pipelines can be extensive, particularly in an animation studio.Hence, the system 100 inputs models from several standard types ofrepresentations including triangle models, implicit functions, CSGmodels, Bezier patches and scanned data, and outputs triangle models.Converting most of the above representations to ADFs is described byFrisken et al.

[0152] This description focuses on two important new developments: amethod for generating ADFs from scanned range data which advances thestate of the art, and a method for triangulating ADFs that generatestopologically consistent LOD triangle models in a fraction of a second.

[0153] Input from Range Data

[0154] There are several commercial systems available for convertingscanned data to triangle models. One approach for importing ADFs intothe system would be to convert the scanned data to triangle models andthen convert the triangle models to the ADFs 10. However, experienceindicates that the triangle models produced by the conversion fromscanned data are often problematic, containing holes, flipped triangles,and overlapping surfaces. Instead, the present system generates the ADF10 directly from the scanned data.

[0155] Several recent research papers have presented methods forconverting scanned data to triangle models that make use of signeddistance fields for more robust, watertight surface reconstructions. Forexample, the method as described by Curless et al. in “A VolumetricMethod for Building Complex Models from Range Images,” Proc. SIGGRAPH'96, pp. 303-312, 1996, is the basis for the data conversion method usedby the Cyberware scanning system. Wheeler, in “Automatic Modeling andLocalization for Object Recognition,” Ph.D. thesis, Carnegie MellonUniversity, 1996, describes a method that uses a true Euclidean distancefunction, and a more volume-centric approach.

[0156] There, the scanned data consist of a set of overlapping 2Dscanned range images taken from different viewpoints. Each range imageis converted to a range surface triangle mesh, and all of the trianglemeshes are imported into the same coordinate system. Wheeler thengenerates a 3-color octree of the distance field in a top-down manner bycomputing the signed distance from volume elements to each rangesurface, and combines the distances using a probability-weightedfunction.

[0157] The probability function depends on the angle of eachcontributing triangle with the original scan direction, the location ofthe triangle relative to the edge of its scanned image, the degree ofagreement between distances computed for overlapping range surfaces, andpossibly other factors. As a last step, the Marching Cubes method ofLorensen et al. is applied to all the boundary leaf cells to generate aclosed, assuming it makes use of volume boundaries, watertight trianglesurface from the signed distance volume. The problem with Wheeler'sapproach is that all cells containing the model's surface are subdividedto the same octree level, thereby increasing memory requirements andprocessing time, and also significantly increasing the number oftriangles generated using Marching Cubes.

[0158] The system 100 adapts and enhances Wheeler's method for the ADFs10. His top-down generation of a three-color octree is replaced by theBDT generation as described above. In the ADFs 10, boundary cells arerepresented as a tri-linear field and consequently do not requiresubdivision in flat or near-flat regions of the surface, resulting in asignificant savings over the three-color octree in both memoryrequirements and the number of distance computations.

[0159] After the scanned data are imported into the system, thesculpting system can be used to correct problems in the model. Theproblems can be due to occluded regions, detail lost because ofresolution limits or scanner noise, and rough or broken surfaces atseams between range images. Finally, when desired, the ADF 10 can beconverted into a triangle model using the approach described below.

[0160] As another advantage of the invention, the system 100 generatessignificantly fewer triangles than the prior art methods because thereare significantly fewer cells in the ADFs 10 than in the prior artthree-color octrees. Furthermore, since the ADFs 10 are a hierarchicaldata structure which support the generation of triangles at a specifiedlevel-of-detail, see below, the system 100 can produce a triangle modelwhose size is tuned specifically for an application.

[0161]FIG. 13 shows a method 1300 for inputting scanned data from ascanner or range finder 1301. The scanner produces range images (R₁, . .. , R_(N)) 1302. The range images are converted 1303 to range meshes1304 in a single coordinate system. Using a probability function 1305,the range meshes are converted to the ADF 1306 using the BDT generator103. The probability function determines the contribution (weight) ofeach vertex in each mesh to the corresponding cell in the ADF. Theeditor 104 can then be applied to correct problems with occlusions,noise, lost detail, etc., to produce the ADF 10.

[0162] Conversion to Triangles

[0163] The present system 100 also provides a new method fortriangulating the ADFs 10 for rendering, control point-based editing,and conversion to output models that can be integrated into an existinganimation pipeline. The triangulation method produces topologicallyconsistent triangle models from an implicit function sampled on anadaptive grid, such as the ADF's octree. The method is very fast and canproduce triangle models in real-time. The method can be used inconjunction with the ADF data structure to produce LOD models asdescribed below.

[0164] Unlike the prior art surface net approach, see citation below,the enhanced method in the present system generates a triangle mesh fromdistance values sampled on an adaptive grid. This presents a specialproblem because neighboring cells in the ADF can have largely varyingsizes. This means that vertices can appear almost anywhere on the commonedges of neighboring cells. Connecting these unpredictably placedvertices, in real-time, to form “quality” triangles is heretofore anunsolved problem.

[0165] The new method is based on a surface net method that wasdeveloped as an alternative to Marching Cubes for building globallysmooth but locally accurate triangle models from binary volume datasampled on a regular grid, see Gibson, “Using distance maps for smoothsurface representation in sampled volumes,”Proc. 1998 IEEE VolumeVisualization Symposium, pp. 23-30, 1998. However, that method uses aniterative energy minimizing process, while moving triangle vertices.That takes a considerable amount of time. In contrast, the new methodaccording to the invention moves vertices to be substantially on thesurface of the model in a single step.

[0166] The present method produces triangle vertices that lie on themodel's surface, and “good quality” triangles, i.e., triangles that areclose to equilateral. Further, as described below, the new method easilydeals with the crack problem typically associated with adaptive grids.In other words, the new method produces triangle models that arewatertight.

[0167] The basic three steps of the method are as follows.

[0168] First, each boundary (surface) leaf cell of the ADF is assigned avertex that is initially placed at the center location of a cell.

[0169] Second, vertices of neighboring cells are connected to formtriangles using the following constraints to produce a topologicallyconsistent “watertight” mesh:

[0170] (1) all triangles are connected by vertices of three neighboringcells that share a common edge, hence, triangles are associated withcell edges; and

[0171] (2) a triangle is associated with an edge only if that edge has azero crossing of the distance field, i.e., the surface intersects theedge.

[0172] Third, after all of the triangles have been formed, trianglevertices are moved towards the cell's surface, i.e., in the direction ofthe ADF gradient, with a single step size equal to the distance value.

[0173] To improve the accuracy and geometry of the mesh, trianglevertices can be moved over the surface, towards neighboring vertices, toimprove the overall quality of the triangles.

[0174] The basic steps of the preferred triangulation method 1400 areshown in FIG. 14. Step 1401 traverses the ADF octree used to store thedata values of the ADF 10 to select candidate cells using candidateselection parameters 1420. In one embodiment of the invention, thecandidate selection parameters 1420 specify that all boundary leaf cellsbe selected as candidate cells. In another embodiment of the invention,the candidate selection parameters 1420 specify that only those boundaryleaf cells whose maximum error measure satisfies a user-specifiedthreshold are selected as candidate cells. Cells below the selectedcells in the ADF octree hierarchy are ignored. In another embodimentboth the depth in the hierarchy, and the error measure can be used toselect candidate cells.

[0175] Step 1402 associates vertices with each candidate cell, and setsthe vertices to the center of the cells. Step 1403 determines if thereare any more candidate cells to be processed. If not, then step 1404relaxes each vertex towards the surface of the cell in a directiontowards the “average” neighboring vertex, and along a tangent planecontaining the relaxed position. Otherwise, for each of the six edges(step 1405), step 1406 determines if the surface crosses an edge. Iftrue, step 1407 determines the vertices V0, V1, and V2 of the triangleassociated with the edge, see description below, and step 1408determines the triangle's orientation from the edge.

[0176] In step 1407, vertex V0 is set to the cell's associated vertex,typically the cell's center point. The vertices V1 and V2 are determinedby the method getFaceNeighborVertex( ). Note, the edge has twoneighboring faces, face1 and face2. To determine the vertex V1,getFaceNeighborVertex( ) takes the edge and face1 as input, and sets thevertex V1 to either the vertex of the cell's face-adjacent neighbor ifthe face-adjacent neighbor is the same size or larger than the cell, orelse, the vertex of the unique child cell of the face-adjacent neighborthat is both adjacent to the face and has a zero-crossing on the edge.Similarly, to determine the vertex V2, getFaceNeighborVertex( ) takesthe edge and face2 as input, and sets the vertex V2 to either the vertexof the cell's face-adjacent neighbor if the face-adjacent neighbor isthe same size or larger than the cell, or else, the vertex of the uniquechild cell of the face-adjacent neighbor that is both adjacent to theface and has a zero-crossing on the edge.

[0177]FIG. 15 shows one possibility of considering only six out oftwelve edges for a 3D cell, e.g. the edges meet at opposing diagonalcorners 1501-1502.

[0178] Most prior art methods for triangulating sampled implicitfunctions generate triangle vertices on cell edges and faces, see forexample, Bloomenthal, “Polygonization of Implicit Surfaces,” ComputerAided Geometric Design, 5(00): pp.341-355, 1988, and Karron et al. “Newfindings from the SpiderWeb algorithm: toward a digital Morse theory,”Proc. Vis. in Biomedical Computing, pp.643-657, 1994.

[0179] As shown in 2D in FIG. 16a, prior art methods can cause cracks inthe triangulated surfaces 1602 where cells of two different sizes meetwhen the implicit function is adaptively sampled. This is because theinterpolated vertex position of one cell may not match the interpolatedposition of its connected neighboring cell. These problems can beaddressed in several ways, but in general, prior art solutions addsignificant complexities to triangulation methods.

[0180] In contrast, in the enhanced method of the present system,triangle vertices are generated at cell centers, and triangles can crossthe faces and edges of different sized cells. Thus, the type of cracksshown in FIG. 16a do not appear. However, cracks may appear in thetriangulated surface when the number of edge crossings between twoneighboring sets of cells differs as illustrated in FIG. 16b.

[0181] This type of crack can be prevented by a pre-conditioning of theADF during generation, or prior to triangulation. The pre-conditioningstep compares the number of zero-crossings of the iso-surface acrossfaces of boundary leaf cells to the total number of zero-crossings forthe associated iso-surface of their face-adjacent neighbors.

[0182] When the number of zero-crossings are not equal, the cell issubdivided using distance values from its face-adjacent neighbors untilthe number of zero-crossings match. For example, the 2D cell on the topin FIG. 16b has no zero-crossings on its bottom edge while theedge-adjacent neighbors have a total of two zero crossings for the sameedge. During pre-conditioning, the cell on the top is furthersubdivided.

[0183] The present system 100 also takes advantage of ADF's hierarchicaldata structure to produce LOD models. Rather than seeding trianglevertices in boundary leaf cells, the hierarchical data structure istraversed and vertices are seeded into boundary cells whose maximumerror measure, computed during generation or editing, satisfy auser-specified threshold. Cells below these cells in the hierarchy areignored. The error threshold can be varied continuously enabling finecontrol over the number of triangles generated in the LOD model.

[0184] Unlike most prior triangle decimation algorithms, the time toproduce an LOD model, as described herein, is proportional to the numberof vertices in the output mesh rather than the size of the input mesh.Generation times are orders of magnitude better than possible with priorart methods. The system 100 can generate a 200,000 triangle model in0.37 seconds, and a 2000 triangle model in less than 0.010 seconds on adesktop system with a Pentium IV class processor.

[0185] Effects of the Invention

[0186] The present system integrates a powerful shape representation,with existing production pipelines that are used for digital characterdesign and animation. The system is intuitive to use, expressive in theresolution and quality of detail that can be achieved, and efficient inmemory usage and processing.

[0187] Described are methods that take ADFs beyond the concept stageinto a practical, working system. These include: innovations in thevolumetric sculpting interface that take advantage of the distance fieldand provide more control to the user, efficient generation and editingalgorithms with reduced memory requirements, better memory coherency andreduced computation, several new rendering approaches that takeadvantage of hardware acceleration in standard PCs, and a very fastmethod for generating topologically consistent LOD triangle models fromADFs.

[0188] Although the invention has been described by way of examples ofpreferred embodiments, it is to be understood that various otheradaptations and modifications may be made within the spirit and scope ofthe invention. Therefore, it is the object of the appended claims tocover all such variations and modifications as come within the truespirit and scope of the invention.

We claim:
 1. A method for converting an adaptively sampled distancefield of a graphics model to a triangle model, the adaptively sampleddistance field including a plurality of surface cells storing distancevalues having corresponding gradients, comprising: assigning a vertex toa center location of each surface cell; connecting the vertices ofneighboring surface cells to form triangles while satisfying apredetermined constraint; and moving each vertex, in a single step, to anew location according to the distance value and corresponding gradientof the vertex to substantially conform the triangles to a surface of themodel.
 2. The method of claim 1 wherein each surface cell has edgesconnecting corners of the cells, and some neighboring surface cells havecommon edges and the predetermined constraint further comprises: onlyconnecting vertices in three neighboring surface cells having commonedges, and at least one common edge intersects the surface of thegraphics model.
 3. The method of claim 2 further comprising; deriving anorientation for each triangle from an orientation of the at least onecommon edge intersecting the surface.
 4. The method of claim 2 furthercomprising: considering less than all common edges of a particularsurface cell when connecting the vertices.
 5. The method of claim 4wherein the considered edges connect to two diagonally opposing cornersof the surface cell.
 6. The method of claim 1 wherein the adaptivelysampled distance field includes a root surface cell, intermediatesurface cells, and leaf surface cells arranged in layers of ahierarchical tree, and wherein vertices are assigned only to leaf cells.7. The method of claim 1 wherein the adaptively sampled distance fieldincludes a root surface cell, intermediate surface cells, and leafsurface cells arranged in layers of a hierarchical tree, and whereinvertices are assigned to all surface cells up to a predetermined levelin the hierarchical tree.
 8. The method of claim 1 wherein theadaptively sampled distance field includes a root surface cell,intermediate surface cells, and leaf surface cells arranged in layers ofa hierarchical tree, and each c ell has an associated error measure, andthe vertices are assigned to cells having a particular error measureless than a predetermined threshold.